Finely chop one small white onion and saute it in some oil over medium heat in a two-to three-quart heavy saucepan. Let the onion cook, stirring it occasionally with a wooden spoon, until it smells good and appears translucent.
Pour the Arborio rice into the saucepan and stir to mix with the onions. Let the rice toast in the pan for a minute or two--it will absorb the flavor from the onions.
While the rice is toasting, heat the vegetable or chicken broth in a separate saucepan over medium heat to a gentle simmer.
Using a ladle, add a cup or two of simmering broth to the rice, then stir the rice until it has absorbed the broth. Keep adding broth to the rice and stirring; this cooking technique helps bring the starch out of the rice to combine with the broth for the creamy texture typical of a classic risotto.
You may not need to use all the broth, so when about three-quarters of the broth has been absorbed (usually 15-20 minutes), start tasting the risotto between additions of broth to see if it's done. When it's done, the individual rice grains should still be distinguishable, and their texture should be slightly firm (al dente), but not at all crunchy.
Add in cooked asparagus and mushrooms, grate in real Parmesan cheese, and add salt and pepper to taste.